A Bayesian method for finding interactions in genomic studies

An important step in building a multiple regression model is the selection of predictors. In genomic and epidemiologic studies, datasets with a small sample size and a large number of predictors are common. In such settings, most standard methods for identifying a good subset of predictors are unstable. Furthermore, there is an increasing emphasis towards identification of interactions, which has not been studied much in the statistical literature. We propose a method, called BSI (Bayesian Selection of Interactions), for selecting predictors in a regression setting when the number of predictors is considerably larger than the sample size with a focus towards selecting interactions. Latent variables are used to infer subset choices based on the posterior distribution. Inference about interactions is implemented by a constraint on the latent variables. The posterior distribution is computed using the Gibbs Sampling methods. The finite-sample properties of the proposed method are assessed by simulation studies. We illustrate the BSI method by analyzing data from a hypertension study involving Single Nucleotide Polymorphisms (SNPs)